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Monday, April 9, 2012

The ISW mystery III: How did the CMB get so hot?

An example map of what the ISW effect would look like on the sky if we could observe it directly (arxiv:1003.0974)

This is probably my most technical post to date. I don't want my contributions to this blog to be (all the time) popularised, ready to consume, pieces of quirky science. I want you to know what we, the cosmologists, are thinking and wondering about each day, beyond just vague explanations about accelerated expansion, dark energy and dark matter. I want you to understand how we're trying to explore the mysteries of cosmology. What are we measuring, how are we measuring it and what are we hoping it will tell us? Doing this has to be a two-way process. I invest time writing, doing my best to make things like the Integrated Sachs-Wolfe effect understandable and you invest time and concentration trying to understand.

The benefit for you of doing this is great. You will become engaged in the science in real time. When the mystery I'm about to reveal finally gets solved you will already be there waiting, expecting. You will be able to bask in the wonder of the discovery during the moments of discovery. Hence, it will also be your discovery.

You will only get this though, if you concentrate and think and read this post through. So, if you don't get it the first time, think about it and read it again. And, if you are left confused by anything, ask!

Recap of earlier posts

I'm going to describe in this post why there is an “ISW mystery”. I described in this post that the integrated Sachs-Wolfe (ISW) effect is the subtle heating and cooling of light as it passes through over and under-dense regions/structures in the universe. For most of the universe's history this effect was effectively non-existent. Any energy gained by light falling into a structure in the universe was perfectly balanced by the energy lost by the light climbing out of the structure. However, late in the universe's history something starts pushing the universe apart and as a result there is a net energy change. The gravitational well is smaller when the light leaves the structure than when it goes in.

Then, in this post, I explained that the ISW effect is incredibly small. This makes observing it very difficult. We can't observe it directly by looking at light from galaxies, quasars, supernovae, stars, etc. because we don't know the temperature of the light's source well enough. In fact, there is only one source of light that we do know well enough to use it to detect the ISW effect. This is the cosmic microwave background (CMB), which I introduce here. Unfortunately, even the tiny fluctuations in the temperature of the CMB are of the same size as the expected ISW temperature shifts. So, we still can't observe the ISW effect directly. What we can do though, is observe it on average. We know that the ISW effect occurs as light travels through over and under-dense regions in space. So what we can do is look for over and under-densities and ask whether the CMB is hotter on average when it has passed through an over-density and colder on average when it has passed through an under-density. How to find structures in space and what I mean by on average is covered in the post you are about to read...

To measure the ISW effect we first need to find where the universe is over and under-dense. Immediately, there is a big roadblock. 80% of the mass in the universe is dark matter. It's called dark matter because we can't see it. So, in order to measure this almost negligible ISW effect, we first have to find invisible structures. Great!

Thankfully, gravity comes to the rescue. Dark matter might be dark, but its behaviour under gravity is exactly the same as any other matter (that's how we know it is there). If 80% of the matter in the universe is dark, then 20% isn't and that 20% is attracted by the invisible 80%. What we can see are galaxies and galaxies form in wells of dark matter. Therefore, in regions where we see more galaxies we know there is also likely to be more matter. In fact, the expected number of galaxies in a region is directly proportional to the matter density in the region. If you double the density, then, on average, you double the number of galaxies. This means that we need only count the number of galaxies in a region of space to determine the likely density of the matter in the region.

Unfortunately, this is only true on average because not every matter well has a galaxy in it and the wells that do have galaxies in them don't all have the same mass. There will be regions of the universe where there is slightly more mass than the average, but fewer galaxies happened to form there, and vice versa.

Cross-correlating maps of the universe

So, there we go. That is how you measure the ISW effect. Simply find galaxies (we've seen many millions of them), count them, and find out whether, on average, the CMB is hotter when it is has travelled through regions with more galaxies and colder when it has travelled through regions with fewer galaxies.

How does such a measurement actually work? To answer that, lets remind ourselves what the CMB is. It is the cosmic microwave background. That is, a radiation field that is a relic left over from the big bang. The CMB permeates all of space. But, we can only measure it at one location, which is here, at Earth. At Earth, we can measure the CMB in every direction on the sky. When we do, what we are seeing is light that has travelled, from the initial hydrogen plasma, through all the space along that line of sight, to Earth. In other words, the regions of the universe that a patch of the CMB has travelled through are the regions behind it on the sky.

Now, just like we can make maps of the Earth, we can make maps of the sky. The most obvious way to look for an ISW signal is to take a sky-map of the CMB and break it up into individual pixels. Then, in each pixel simply count the number of galaxies along that line of sight and from that make a map of the expected average density of matter along each line of sight. You can see an example of such a map below. If the ISW effect exists, then there should be some sort of positive correlation between these two maps. The hot spots on the CMB map should occur more often in pixels that correspond to over-densities on the density map and the cold spots should occur in pixels that correspond to under-densities.

A map of the density contrast calculated from luminous red galaxies in the SDSS catalogue (arxiv:0911.1352).

The process of quantifying how well any two maps are correlated is a bit technical. The precise details aren't important to understanding the mystery so I won't explain it here. If a reader is super-keen to know how this is done, let me know and I will either explain in a future post, find an appropriate guest-poster, or direct those who are curious to some relevant literature.

What is important though is that some groups have made measurements of this type. The results of these measurements are mixed, but are more or less consistent with each other and what we expect. There does appear to be a tendency for the measured signal to be slightly larger than the expected signal. This might, at first, appear interesting; however, don't forget that both of the maps used in the measurement have sources of noise. The CMB temperature map has the primordial CMB anisotropies and the density map has the uncertainty introduced by the fact that the number of galaxies doesn't perfectly trace out the total matter density. Purely by chance, these sources of noise can have correlations with each other and with the actual ISW effect. These chance correlations will either enhance or shrink the signal. Thankfully, the size of this effect can be quantified and has been for each measurement. The result is that the enhancement seen in each measurement, relative to the expected signal, is consistent with an enhancement arising from the noise.

Everything appears fine then, right? The ISW effect has been measured and is giving the results we expect.

Not so fast...

Getting extreme

The biggest problem with the measurements to date is the small number of galaxies that we have observed (and that we know are definitely galaxies). The CMB measurements, by comparison are almost ideal. In the future, after experiments like Euclid have found many, many more galaxies, this problem will go away but we're stuck with it for now.

But maybe we're not completely stuck with it. Here we get to the source of the mystery, a clever measurement made by a group in Hawaii. The problem that comes from only having a small number of galaxies is the uncertainty in what the actual matter density is in any region of space. In most regions of the universe, the density will be very close to the average density. Therefore, this uncertainty could easily result in an over-dense region being labelled as under-dense, which is a big problem. But what if we only look at the most extreme regions of the universe? Think about the most over-dense region in the entire observable universe. Even though there will still be a large uncertainty in the exact density of matter in that region, we can still be pretty sure that the number of galaxies in the region will be greater than average. The same is true for the most under-dense region and the fact that the number of galaxies in the region will definitely be less than average.

What this group in Hawaii did was to consider the ISW effect arising from only these most extreme regions. They used an algorithm that finds the regions of the universe with more galaxies than average (or less galaxies than average) and quantifies the probability that these regions are actually over-dense (or under-dense). They then studied only the regions which are almost certainly actually over-dense (or actually under-dense).

The patches in a map of the CMB that have the most extreme over and under-dense regions in the universe lying behind them (arXiv:0805.2974)

On Earth, each one of these regions will lie in the direction of some particular point in the sky (seen in the figure above). What the group did next was to look at four square degree patches lying around each one of these points on a CMB map. Now, if you believe in an ISW effect you should expect that the patches lying in front of over-dense regions will be hotter on average than those lying in front of under-dense regions. How can we see this (keep concentrating, we're almost there)?

The problem is that even though we're almost certain that the temperature fluctuations in these patches will have some contribution from the ISW effect, there is still the primordial CMB noise to deal with. To get the ISW signal to dominate over the CMB noise the group first stacked all the “over-dense” patches on top of each other, pixel by pixel. Then, they formed a new four square degree patch by calculating the average temperature in each pixel of this stacked image. The CMB noise should be completely random, sometimes hotter sometimes colder. However, the ISW effect coming from the over-dense regions should always be hotter. Therefore, while the CMB noise should hopefully cancel itself out, the ISW signal should accumulate. The exact same process was done separately for the “under-dense” patches.

Stacked images of the patches of CMB lying in front of extreme over-dense ("clusters") and under-dense ("voids") regions (arXiv:0805.3695).

The figure above is the result that they got. Clearly, the “over-dense” patch has a hot blob in the middle and the “under-dense” patch has a cold blob. Awesome! The ISW effect has been detected, well done Hawaii. Time to update the wikipedia page, pack our bags and head home, right?

But, where is the mystery?

Well, precisely how hot is that hot spot and precisely how cold is that cold spot?

And, this is it, at last we get to the mystery. When you take those two patches and calculate the average temperature in each of them you find that the hot spot has a temperature of 8 micro Kelvin and the cold spot has a temperature of -11 micro Kelvin. The noise that will be remaining from the primordial CMB is approximately 3 micro Kelvin in amplitude.

The mystery is this: in the standard model of cosmology, the maximum possible value for the temperature shift caused by the ISW effect from individual over-dense regions is just 1.5 micro Kelvin (and -1,5 micro Kelvin for under-dense regions). That is, even if the regions selected by this Hawaiian group's algorithm really were the regions that give the biggest possible ISW signal, it should be much, much smaller than what they've seen.

And that's it. The CMB that has travelled through a selection of the most extreme over and under-dense regions of the universe has been heated by the over-dense regions and cooled by the under-dense regions much more than what is expected in the standard model. That is the mystery.

So what is going on? Something, somehow is heating and cooling the CMB in these patches. It can't be the ISW effect in the standard model of cosmology, it's too small. It can't be the primordial CMB either, because that's too small too. This means that any other explanation requires either new physics or something fishy to be occurring in the CMB map.

Now the fact that almost all the correlation measurements mentioned earlier seem to have a slightly larger signal than what is expected starts to seem very curious.

So, where to now?

In the next post I will get into the exciting stuff. I'll explain in a bit more detail why we expect the signal to be so much smaller than the observation, but then I'll go into what some of the candidates are for resolving the mystery (as well as what the greater implications for cosmology and high energy physics are for each candidate solution).

The possibilities include (amongst other options): modifying the initial conditions of the big bang, modifying the way we think gravity works and modifying how we think dark energy behaves.

8 comments:

Maybe this is something you have introduced in detail in your previous posts on the CMB, or maybe as a cosmologist it seems so obvious to you that you forgot to mention it, or maybe you did mention it somewhere and my eye skipped over it ...

... but I think it is worth emphasising that when you talk about "sky-maps of the CMB" what you mean is maps showing the temperature of the CMB radiation in different directions. Or rather, the difference between the temperature in a direction and the average temperature. So each pixel records this difference in temperatures in that direction. Similarly in a "galaxy map" each pixel records the excess number of galaxies in that pixel area over the average for all pixels.

Thanks for the comment Sesh. I did find this article to be quite hard to write, so I will really appreciate any clarifying comments you can add.

It's interesting that you happen to bring up the maps as well. I did feel when writing that I had struggled to explain coherently what a sky map is. So thanks for helping to clarify it.

For everyone else, I'll add even more clarification to Sesh's comment above. Firstly, I expect that everyone reading this understands what a map of the Earth's surface looks like (i.e. this). Imagine now that the Earth is a perfect sphere. If you take each point on the Earth and associate to it the point in the sky that you would see if you looked directly up then you can also draw a map of the sky. The map of the sky is exactly the same as the map of the Earth, with each pixel on the Earth map replaced by the corresponding sky pixel defined by my previous sentence.

So then, you can construct the maps relevant to the ISW effect, by counting galaxies or measuring the CMB temperature in the direction of any of these sky pixels.

I hope that makes sense, but again, if it doesn't, please ask questions.

Nice post, Shaun. I reached the end slightly confused* though. It seems that you are measuring one quantity (the temperature of the CMB), but trying to extract two pieces of information, i.e., the primordial fluctuations, and the ISW effect.

But I think maybe now I understand. The fluctuations in the 'bare' CMB (before it propagates through the universe) reveal the density perturbations at the surface of last scattering. The ISW effect depends, roughly speaking, on the average density along our line of sight. There is no reason for the density at the surface of last scattering to be correlated with the average density all the way along our line of sight, so if we compare many regions of the sky, the primordial fluctuations should cancel out, leaving just the ISW effect. And this was the whole point! Does that sound right?

*This is not a comment on the clarity of your explanation; I feel like I am always confused.

Or, at least, that's exactly what *should* be happening, in principle. But it can't be just the standard ISW effect left over in the actual observation because the standard ISW effect is too small. Either that or one of the seemingly benign assumptions in the theoretical calculation isn't valid. But it is very hard to see what that assumption could be (hopefully I'll be able to make a convincing case of this in the next post).

I'd make the additional point that the statistical distribution of density perturbations along the line of sight does depend on the primordial perturbations (and how these perturbations have grown under gravity - which is luckily relatively simple to describe at the linear level because different Fourier modes evolve independently). Of course this growth or evolution of potential wells is exactly the ISW effect.

So the point I thought you were going to make is correct even though you didn't end up saying it explicitly - the detailed observation of an ISW-like correlation can only be used to test one of two hypotheses. Either you assume the spectrum of primordial perturbations and test their time evolution, or your assume the time evolution and constrain the primordial distribution, but it is hard to constrain both. This is a common problem in cosmology!